Answer:
[tex]m\angle A= 30^{\circ}[/tex]
Step-by-step explanation:
In the question, we're given [tex]\angle A\cong \angle D[/tex]. Therefore, the measure of these two angles must be equal.
To find the value of [tex]x[/tex], set these two angles equal to each other:
[tex]4x-26=x+16[/tex]
Add 26 and subtract [tex]x[/tex] from both sides:
[tex]3x=42[/tex]
Divide both sides by 3:
[tex]x=\frac{42}{3}=14[/tex]
Since [tex]\angle A[/tex] was labelled as [tex]4x-26[/tex], substitute [tex]x=14[/tex] to find its measure:
[tex]\angle A=4(14)-26,\\\angle A=56-26,\\\angle A=\boxed{30^{\circ}}[/tex]
You can also substitute [tex]x=14[/tex] into the label of angle D as angle A is congruent to angle D for easier calculations ([tex]14+16=\boxed{30^{\circ}}[/tex]).
